{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "169445ad",
   "metadata": {},
   "source": [
    "# via. [MCMC: A (very) Beginnner’s Guide](https://prappleizer.github.io/Tutorials/MCMC/MCMC_Tutorial.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8bcaab38",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import emcee\n",
    "import corner\n",
    "import pandas as pd\n",
    "from scipy.optimize import minimize\n",
    "from IPython.display import display, Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "23fad323",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_csv = pd.read_csv('https://gitee.com/Astro-Lee/storage/raw/master/data/A(T)_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "718c4f17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>A</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>50</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>70</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>80</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>80</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>90</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>90</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>90</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>95</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>100</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>100</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>100</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>105</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>105</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>110</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>110</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>110</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>115</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>115</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>115</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>120</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>120</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>120</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>125</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>130</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>130</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>135</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>135</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>140</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>140</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>145</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>150</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>150</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>155</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>155</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>160</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>160</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>160</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>165</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>170</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>180</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      T   A\n",
       "0    50  19\n",
       "1    60  20\n",
       "2    60  21\n",
       "3    70  17\n",
       "4    70  22\n",
       "5    80  25\n",
       "6    80  28\n",
       "7    90  21\n",
       "8    90  25\n",
       "9    90  31\n",
       "10   95  25\n",
       "11  100  30\n",
       "12  100  29\n",
       "13  100  33\n",
       "14  105  35\n",
       "15  105  32\n",
       "16  110  30\n",
       "17  110  28\n",
       "18  110  30\n",
       "19  115  31\n",
       "20  115  36\n",
       "21  115  30\n",
       "22  120  36\n",
       "23  120  25\n",
       "24  120  28\n",
       "25  125  28\n",
       "26  130  31\n",
       "27  130  32\n",
       "28  135  34\n",
       "29  135  25\n",
       "30  140  26\n",
       "31  140  33\n",
       "32  145  31\n",
       "33  150  36\n",
       "34  150  33\n",
       "35  155  41\n",
       "36  155  33\n",
       "37  160  40\n",
       "38  160  30\n",
       "39  160  37\n",
       "40  165  32\n",
       "41  170  35\n",
       "42  180  38"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5304cca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data_csv['T']\n",
    "y = data_csv['A']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ab24d17d",
   "metadata": {},
   "outputs": [],
   "source": [
    "yerr = 0.05 * np.mean(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "856c55ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = (np.asarray(x), np.asarray(y), yerr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "482b49af",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(theta,x=data[0]):\n",
    "    m, b = theta\n",
    "    model = m * x + b\n",
    "    return model\n",
    "\n",
    "def ln_likelihood(theta, x, y, yerr):\n",
    "    return -0.5 * np.sum(((y - model(theta, x))/yerr) ** 2)\n",
    "\n",
    "def ln_prior(theta):\n",
    "    m, b = theta\n",
    "    if m > 0 :\n",
    "        return 0.0\n",
    "    return -np.inf\n",
    "\n",
    "def ln_probability(theta, x, y, yerr):\n",
    "    lp = ln_prior(theta)\n",
    "    if not np.isfinite(lp):\n",
    "        return -np.inf\n",
    "    return lp + ln_likelihood(theta, x, y, yerr)\n",
    "\n",
    "def sample_walkers(nsamples,flattened_chain):\n",
    "    models = []\n",
    "    draw = np.floor(np.random.uniform(0,len(flattened_chain),size=nsamples)).astype(int)\n",
    "    thetas = flattened_chain[draw]\n",
    "    for i in thetas:\n",
    "        mod = model(i)\n",
    "        models.append(mod)\n",
    "    spread = np.std(models,axis=0)\n",
    "    med_model = np.median(models,axis=0)\n",
    "    return med_model,spread\n",
    "\n",
    "def maximum_likelihood_estimation(ln_likelihood, data):\n",
    "    \"\"\"\n",
    "    ln_likelihood: ln_likelihood函数;\n",
    "    \n",
    "    \"\"\"\n",
    "    p_m, p_b = np.polyfit(data[0], data[1], deg=1)\n",
    "    nll = lambda *args: -ln_likelihood(*args)\n",
    "    initial = np.array([p_m, p_b])#m, b的初值\n",
    "    soln = minimize(nll, initial, args=data)#最大似然m, b的值为soln.x\n",
    "    return soln.x\n",
    "\n",
    "def plotter(sampler,data):\n",
    "    samples = sampler.flatchain\n",
    "    med_model, spread = sample_walkers(100,samples)\n",
    "\n",
    "    theta_max  = samples[np.argmax(sampler.flatlnprobability)]\n",
    "    best_fit_model = model(theta_max)\n",
    "\n",
    "    plt.figure(dpi=300)\n",
    "    plt.errorbar(data[0],data[1],yerr=data[2],fmt='k.',lw=1,ms=4)\n",
    "    plt.plot(data[0],best_fit_model,label='Highest Likelihood Model',lw=1)\n",
    "    plt.fill_between(data[0],med_model-spread,med_model+spread,color='grey',alpha=0.5,label=r'$1\\sigma$ Posterior Spread')\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "def display_latex(samples, labels):\n",
    "    for i in range(len(labels)):\n",
    "        mcmc = np.percentile(samples[:, i], [16, 50, 84])\n",
    "        q = np.diff(mcmc)\n",
    "        txt = \"\\mathrm{{{0}}} = {1:.2f}_{{-{2:.2f}}}^{{+{3:.2f}}}\"\n",
    "        txt = txt.format(labels[i], mcmc[1], q[0], q[1])\n",
    "        display(Math(txt))\n",
    "\n",
    "def main(p0,nwalkers,nsteps,ndim,ln_probability,data):\n",
    "    sampler = emcee.EnsembleSampler(nwalkers, ndim, ln_probability, args=data)\n",
    "\n",
    "    print(\"Running burn-in...\")\n",
    "    p0, _, _ = sampler.run_mcmc(p0, 100)\n",
    "    sampler.reset()\n",
    "\n",
    "    print(\"Running production...\")\n",
    "    pos, prob, state = sampler.run_mcmc(p0, nsteps, progress=True)\n",
    "\n",
    "    return sampler, pos, prob, state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ea673624",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(dpi=300)\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.errorbar(data[0],data[1],yerr=data[2],fmt='k.',lw=1,ms=4)\n",
    "ax1.set_xlabel('X')\n",
    "ax1.set_ylabel('Y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0c2de588",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.13076843, 14.41064881])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = maximum_likelihood_estimation(ln_likelihood, data)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2140c294",
   "metadata": {},
   "outputs": [],
   "source": [
    "nwalkers = 128\n",
    "nsteps = 5000\n",
    "ndim = len(p)\n",
    "p0 = [np.array(p) + 1e-2 * np.random.randn(ndim) for i in range(nwalkers)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "18ebe0a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running burn-in...\n",
      "Running production...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████████████████████████████████████████| 5000/5000 [00:19<00:00, 254.57it/s]\n"
     ]
    }
   ],
   "source": [
    "sampler, _, _, _ = main(p0,nwalkers,nsteps,ndim,ln_probability,data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "448e8b6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotter(sampler,data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "20661dfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = ['m','b']\n",
    "fig = corner.corner(sampler.flatchain,show_titles=True,labels=labels,plot_datapoints=True,quantiles=[0.16, 0.5, 0.84],smooth=True,fig=plt.figure(dpi=100),title_fmt='.3f',truths=p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "24200276",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathrm{m} = 0.13_{-0.01}^{+0.01}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathrm{b} = 14.41_{-0.86}^{+0.85}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_latex(sampler.flatchain, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a11059b8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
